五角形镶嵌的可能性

五角形镶嵌的可能性
几何画板及绘图内容加载中,请稍等……
2014-08-30 09:20
这个范例展示了五角形镶嵌的可能性。它涉及组合数学中的几何构造,通过使用Pentagrin1, Pentagrin2等命令,可以构造出多种五角形镶嵌图案。该范例适合高中及以上学生,用于探索几何变换和镶嵌理论。

GeoGebra 命令及参数

  1. Pentagrin1(A, B) → poly1, a, b, c, d, e, C, D, E
  2. Pentagrin1(E, D) → poly2, f, g, h, i, j, F, G, H
  3. Pentagrin1(H, G) → poly3, k, l, m, n, p, I, J, K
  4. Pentagrin1(K, J) → poly4, q, r, s, t, a_1, L, M, N
  5. Pentagrin1(N, M) → poly5, b_1, c_1, d_1, e_1, f_1, O, P, Q
  6. Pentagrin1(Q, P) → poly6, g_1, h_1, i_1, j_1, k_1, R, S, T
  7. Pentagrin1(T, S) → poly7, l_1, m_1, n_1, p_1, q_1, U, V, W
  8. Pentagrin1(W, V) → poly8, r_1, s_1, t_1, a_2, b_2, Z, A_1, B_1
  9. Pentagrin1(B_1, A_1) → poly9, c_2, d_2, e_2, f_2, g_2, C_1, D_1, E_1
  10. Pentagrin1(E_1, D_1) → poly10, h_2, i_2, j_2, k_2, l_2, F_1, G_1, H_1
  11. Pentagrin2(G, D) → poly11, m_2, n_2, p_2, q_2, r_2, I_1, J_1, K_1
  12. Pentagrin2(G, K_1) → poly12, s_2, t_2, a_3, b_3, c_3, L_1, M_1, N_1
  13. Pentagrin2(G, N_1) → poly13, d_3, e_3, f_3, g_3, h_3, O_1, P_1, Q_1
  14. Pentagrin2(J, G) → poly14, i_3, j_3, k_3, l_3, m_3, R_1, S_1, T_1
  15. Pentagrin2(J, T_1) → poly15, n_3, p_3, q_3, r_3, s_3, U_1, V_1, W_1
  16. Pentagrin2(J, W_1) → poly16, t_3, a_4, b_4, c_4, d_4, Z_1, A_2, B_2
  17. Pentagrin2(M, J) → poly17, e_4, f_4, g_4, h_4, i_4, C_2, D_2, E_2
  18. Pentagrin2(M, E_2) → poly18, j_4, k_4, l_4, m_4, n_4, F_2, G_2, H_2
  19. Pentagrin2(M, H_2) → poly19, p_4, q_4, r_4, s_4, t_4, I_2, J_2, K_2
  20. Pentagrin2(P, M) → poly20, a_5, b_5, c_5, d_5, e_5, L_2, M_2, N_2
  21. Pentagrin2(P, N_2) → poly21, f_5, g_5, h_5, i_5, j_5, O_2, P_2, Q_2
  22. Pentagrin2(P, Q_2) → poly22, k_5, l_5, m_5, n_5, p_5, R_2, S_2, T_2
  23. Pentagrin2(S, P) → poly23, q_5, r_5, s_5, t_5, a_6, U_2, V_2, W_2
  24. Pentagrin2(S, W_2) → poly24, b_6, c_6, d_6, e_6, f_6, Z_2, A_3, B_3
  25. Pentagrin2(S, B_3) → poly25, g_6, h_6, i_6, j_6, k_6, C_3, D_3, E_3
  26. Pentagrin2(V, S) → poly26, l_6, m_6, n_6, p_6, q_6, F_3, G_3, H_3
  27. Pentagrin2(V, H_3) → poly27, r_6, s_6, t_6, a_7, b_7, I_3, J_3, K_3
  28. Pentagrin2(V, K_3) → poly28, c_7, d_7, e_7, f_7, g_7, L_3, M_3, N_3
  29. Pentagrin2(A_1, V) → poly29, h_7, i_7, j_7, k_7, l_7, O_3, P_3, Q_3
  30. Pentagrin2(A_1, Q_3) → poly30, m_7, n_7, p_7, q_7, r_7, R_3, S_3, T_3
  31. Pentagrin2(A_1, T_3) → poly31, s_7, t_7, a_8, b_8, c_8, U_3, V_3, W_3
  32. Pentagrin2(D_1, A_1) → poly32, d_8, e_8, f_8, g_8, h_8, Z_3, A_4, B_4
  33. Pentagrin2(D_1, B_4) → poly33, i_8, j_8, k_8, l_8, m_8, C_4, D_4, E_4
  34. Pentagrin2(D_1, E_4) → poly34, n_8, p_8, q_8, r_8, s_8, F_4, G_4, H_4
  35. Pentagrin2(B, D_1) → poly35, t_8, a_9, b_9, c_9, d_9, I_4, J_4, K_4
  36. Pentagrin2(B, K_4) → poly36, e_9, f_9, g_9, h_9, i_9, L_4, M_4, N_4
  37. Pentagrin2(B, N_4) → poly37, j_9, k_9, l_9, m_9, n_9, O_4, P_4, Q_4
  38. Pentagrin2(D, B) → poly38, p_9, q_9, r_9, s_9, t_9, R_4, S_4, T_4
  39. Pentagrin2(D, T_4) → poly39, a_{10}, b_{10}, c_{10}, d_{10}, e_{10}, U_4, V_4, W_4
  40. Pentagrin2(D, W_4) → poly40, f_{10}, g_{10}, h_{10}, i_{10}, j_{10}, Z_4, A_5, B_5
  41. Pentagrin2(Z_1, U_1) → poly41, k_{10}, l_{10}, m_{10}, n_{10}, p_{10}, C_5, D_5, E_5
  42. Pentagrin2(Z_1, E_5) → poly42, q_{10}, r_{10}, s_{10}, t_{10}, a_{11}, F_5, G_5, H_5
  43. Pentagrin2(F_2, Z_1) → poly43, b_{11}, c_{11}, d_{11}, e_{11}, f_{11}, I_5, J_5, K_5
  44. Pentagrin2(F_2, K_5) → poly44, g_{11}, h_{11}, i_{11}, j_{11}, k_{11}, L_5, M_5, N_5
  45. Pentagrin2(F_2, N_5) → poly45, l_{11}, m_{11}, n_{11}, p_{11}, q_{11}, O_5, P_5, Q_5
  46. Pentagrin2(I_2, F_2) → poly46, r_{11}, s_{11}, t_{11}, a_{12}, b_{12}, R_5, S_5, T_5
  47. Pentagrin2(I_2, T_5) → poly47, c_{12}, d_{12}, e_{12}, f_{12}, g_{12}, U_5, V_5, W_5
  48. Pentagrin2(O_2, I_2) → poly48, h_{12}, i_{12}, j_{12}, k_{12}, l_{12}, Z_5, A_6, B_6
  49. Pentagrin2(O_2, B_6) → poly49, m_{12}, n_{12}, p_{12}, q_{12}, r_{12}, C_6, D_6, E_6
  50. Pentagrin2(O_2, E_6) → poly50, s_{12}, t_{12}, a_{13}, b_{13}, c_{13}, F_6, G_6, H_6
  51. Pentagrin2(R_2, O_2) → poly51, d_{13}, e_{13}, f_{13}, g_{13}, h_{13}, I_6, J_6, K_6
  52. Pentagrin2(R_2, K_6) → poly52, i_{13}, j_{13}, k_{13}, l_{13}, m_{13}, L_6, M_6, N_6
  53. Pentagrin2(Z_2, R_2) → poly53, n_{13}, p_{13}, q_{13}, r_{13}, s_{13}, O_6, P_6, Q_6
  54. Pentagrin2(Z_2, Q_6) → poly54, t_{13}, a_{14}, b_{14}, c_{14}, d_{14}, R_6, S_6, T_6
  55. Pentagrin2(Z_2, T_6) → poly55, e_{14}, f_{14}, g_{14}, h_{14}, i_{14}, U_6, V_6, W_6
  56. Pentagrin2(C_3, Z_2) → poly56, j_{14}, k_{14}, l_{14}, m_{14}, n_{14}, Z_6, A_7, B_7
  57. Pentagrin2(C_3, B_7) → poly57, p_{14}, q_{14}, r_{14}, s_{14}, t_{14}, C_7, D_7, E_7
  58. Pentagrin2(I_3, C_3) → poly58, a_{15}, b_{15}, c_{15}, d_{15}, e_{15}, F_7, G_7, H_7
  59. Pentagrin2(I_3, H_7) → poly59, f_{15}, g_{15}, h_{15}, i_{15}, j_{15}, I_7, J_7, K_7
  60. Pentagrin2(I_3, K_7) → poly60, k_{15}, l_{15}, m_{15}, n_{15}, p_{15}, L_7, M_7, N_7
  61. Pentagrin2(L_3, I_3) → poly61, q_{15}, r_{15}, s_{15}, t_{15}, a_{16}, O_7, P_7, Q_7
  62. Pentagrin2(L_3, Q_7) → poly62, b_{16}, c_{16}, d_{16}, e_{16}, f_{16}, R_7, S_7, T_7
  63. Pentagrin2(R_3, L_3) → poly63, g_{16}, h_{16}, i_{16}, j_{16}, k_{16}, U_7, V_7, W_7
  64. Pentagrin2(R_3, W_7) → poly64, l_{16}, m_{16}, n_{16}, p_{16}, q_{16}, Z_7, A_8, B_8
  65. Pentagrin2(R_3, B_8) → poly65, r_{16}, s_{16}, t_{16}, a_{17}, b_{17}, C_8, D_8, E_8
  66. Pentagrin2(U_3, R_3) → poly66, c_{17}, d_{17}, e_{17}, f_{17}, g_{17}, F_8, G_8, H_8
  67. Pentagrin2(U_3, H_8) → poly67, h_{17}, i_{17}, j_{17}, k_{17}, l_{17}, I_8, J_8, K_8
  68. Pentagrin2(C_4, U_3) → poly68, m_{17}, n_{17}, p_{17}, q_{17}, r_{17}, L_8, M_8, N_8
  69. Pentagrin2(C_4, N_8) → poly69, s_{17}, t_{17}, a_{18}, b_{18}, c_{18}, O_8, P_8, Q_8
  70. Pentagrin2(C_4, Q_8) → poly70, d_{18}, e_{18}, f_{18}, g_{18}, h_{18}, R_8, S_8, T_8
  71. Pentagrin2(F_4, C_4) → poly71, i_{18}, j_{18}, k_{18}, l_{18}, m_{18}, U_8, V_8, W_8
  72. Pentagrin2(F_4, W_8) → poly72, n_{18}, p_{18}, q_{18}, r_{18}, s_{18}, Z_8, A_9, B_9
  73. Pentagrin2(L_4, F_4) → poly73, t_{18}, a_{19}, b_{19}, c_{19}, d_{19}, C_9, D_9, E_9
  74. Pentagrin2(L_4, E_9) → poly74, e_{19}, f_{19}, g_{19}, h_{19}, i_{19}, F_9, G_9, H_9
  75. Pentagrin2(L_4, H_9) → poly75, j_{19}, k_{19}, l_{19}, m_{19}, n_{19}, I_9, J_9, K_9
  76. Pentagrin2(O_4, L_4) → poly76, p_{19}, q_{19}, r_{19}, s_{19}, t_{19}, L_9, M_9, N_9
  77. Pentagrin2(O_4, N_9) → poly77, a_{20}, b_{20}, c_{20}, d_{20}, e_{20}, O_9, P_9, Q_9
  78. Pentagrin2(U_4, O_4) → poly78, f_{20}, g_{20}, h_{20}, i_{20}, j_{20}, R_9, S_9, T_9
  79. Pentagrin2(U_4, T_9) → poly79, k_{20}, l_{20}, m_{20}, n_{20}, p_{20}, U_9, V_9, W_9
  80. Pentagrin2(U_4, W_9) → poly80, q_{20}, r_{20}, s_{20}, t_{20}, a_{21}, Z_9, A_{10}, B_{10}
  81. Pentagrin2(I_1, U_4) → poly81, b_{21}, c_{21}, d_{21}, e_{21}, f_{21}, C_{10}, D_{10}, E_{10}
  82. Pentagrin2(I_1, E_{10}) → poly82, g_{21}, h_{21}, i_{21}, j_{21}, k_{21}, F_{10}, G_{10}, H_{10}
  83. Pentagrin2(L_1, I_1) → poly83, l_{21}, m_{21}, n_{21}, p_{21}, q_{21}, I_{10}, J_{10}, K_{10}
  84. Pentagrin2(L_1, K_{10}) → poly84, r_{21}, s_{21}, t_{21}, a_{22}, b_{22}, L_{10}, M_{10}, N_{10}
  85. Pentagrin2(L_1, N_{10}) → poly85, c_{22}, d_{22}, e_{22}, f_{22}, g_{22}, O_{10}, P_{10}, Q_{10}
  86. Pentagrin2(O_1, L_1) → poly86, h_{22}, i_{22}, j_{22}, k_{22}, l_{22}, R_{10}, S_{10}, T_{10}
  87. Pentagrin2(O_1, T_{10}) → poly87, m_{22}, n_{22}, p_{22}, q_{22}, r_{22}, U_{10}, V_{10}, W_{10}
  88. Pentagrin2(U_1, O_1) → poly88, s_{22}, t_{22}, a_{23}, b_{23}, c_{23}, Z_{10}, A_{11}, B_{11}
  89. Pentagrin2(U_1, B_{11}) → poly89, d_{23}, e_{23}, f_{23}, g_{23}, h_{23}, C_{11}, D_{11}, E_{11}
  90. Pentagrin2(U_1, E_{11}) → poly90, i_{23}, j_{23}, k_{23}, l_{23}, m_{23}, F_{11}, G_{11}, H_{11}

AI 绘图提示语参考

绘制一个由多个五边形组成的镶嵌图案,使用Pentagrin1和Pentagrin2命令,从点A和B开始,依次构造多个五边形,每个五边形的顶点与前一个五边形的顶点相连,形成一个复杂的镶嵌图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。